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Exam 2-3 Flashcards Preview

Central Limit Theorem

When sampling from a non-Normal population, the sampling distribution of x bar is approximately Normal whenever the sample is large and random

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Sample

A subset of individuals in the population; the group about which we actually collect information.

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Theoretical sampling distribution of x bar

The distribution of all possible samples of the same size from the same population

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Approximate sampling distribution of x bar

The distribution of x bar values obtained from repeatedly taking SRS's of the same size from the same population

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Sampling distribution of x bar 1. Center2. Spread3. Shape

1.mean of x bar = population mean valid for all sample sizes and populations of all shapes2. Stand.deviation of x bar= stand dev of population decided by the square root of n3. Normal -shape of x bar distribution is exactly normal for any n; Non-Normal - shape of sampling distribution of x bar is approximately normal when n (sample size) is large

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Facts about Sampling Distribution of x bar

-Mean= mu regardless of population shape or sample size- standard dev of x bar is always less than the standard deviation of the population for samples of any size where n>1-standard dev of x bar gets smaller as n increases at rate square root of n. To cut stand dev in half, quadruple sample size- Shape is normal if population is normal for any sample size- shape is approximately Normal if we take a large random sample from a non-normal population

A measure of variability of the values of the statistic x bar about mu ; a measure of the variability of the sampling distribution of x bar; in other words the average amount that statistic (x bar) deviates from it's mean. Computed as sigma over square root of n

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Predicting sampling distribution of x bar

Take only one sample of size n Use results to make inference about the populationBecause mean =mu and standard deviation of x bar= sigma over square root of n; and the shape is approx Normal if sample is random and large according to CLT

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R-sq is a fraction of

Variation in the values of y that is explained by the least squares regression of y on x

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Outlier in y direction of a Scatterplot have ...... Residuals but other outliers need not to have large residuals

Large

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Influential observations in x direction of Scatterplot are often ..... For the least-squares regression line